Question

The equation of the linear regression line represents the relationship between the number of laps a person can swim, x, and the number of minutes a person can run, y. yˆ=52x+6 What does the slope of the line represent? For every 5 laps that a person can swim, the number of minutes they can run increases by 2. For every 2 laps that a person can swim, the number of minutes they can run increases by 5. For every 5 laps that a person can swim, the number of minutes they can run decreases by 2. For every 2 laps that a person can swim, the number of minutes they can run decreases by 5.

Answer 1

I am assuming that the equation is: $y= \frac{5}{2}x+6$ based on the answer choices given. As a note, you can write the fraction as (5/2) so that it doesn't just look like 52 (fifty 2).

The equation is written in slope-intercept form. That is, it looks like: $y=mx+b$. When written like this the the number in front of x (called the coefficient) is the slope and the number by itself at the end (called the constant) is the y-intercept. If we graphed the line given by the equation the y-intercept is the y-coordinate of the point where the line crosses the y-axis. Here it is 6 and the point is (0,6).

The slope is $\frac{5}{2}$. So, what does that mean? The slope tells us something about the "steepness" of the line. It gives the "change is y" over the "change in x." That means that every time the change in y is 5, the change in x is 2. Since the y gives the number of minutes one can run and the x gives the number of laps, what a slope of 5/2 means is that for  FOR EVERY 2 LAPS YOU CAN SWIM YOU CAN RUN ANOTHER 5 MINUTES.